In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra ”dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...

Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n } n ∈ N of additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d 0 = I R , the identity map on R and [Formula: see text] holds for all a, b ∈ U and for each n ∈ N. A family F = {f n } n ∈ N of additive mappings f n :R → R is said to be a generalized (σ,τ)- high...

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, show that if B:L?0(G)*x L?0(G)* is asymmetric bi-derivation such [B(m,m),mk] Z(L?0(G)*) for all m (G)*, then B the zero map. Furthermore, characterize generalized biderivations group algebras. We also prove any Jordan 0(G)* a bi-derivation.

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from Mn(A) (A is not necessarily a prime algebra) onto an arbitrary ring R is additive.